text: For an incompressible and isotropic Newtonian fluid in laminar flow only in the direction x (i.e. where viscosity is isotropic in the fluid), the shear stress is related to the strain rate by the simple constitutive equation
  where
  * is the shear stress ("skin drag") in the fluid,
  * is a scalar constant of proportionality, the dynamic viscosity of the fluid
  * is the derivative in the direction y, normal to x, of the flow velocity component u that is oriented along the direction x.
  In case of a general 2D incompressibile flow in the plane x, y, the Newton constitutive equation become:
  where:
  * is the shear stress ("skin drag") in the fluid,
  * is the partial derivative in the direction y of the flow velocity component u that is oriented along the direction x.
  * is the partial derivative in the direction x of the flow velocity component v that is oriented along the direction y.
  We can now generalize to the case of an incompressible flow with a general direction in the 3D space, the above constitutive equation becomes
  where
  * is the th spatial coordinate
  * is the fluid's velocity in the direction of axis 
  * is the -th component of the stress acting on the faces of the fluid element perpendicular to axis . It is the ij-th component of the shear stress tensor
  or written in more compact tensor notation
  where  is the flow velocity gradient.
  An alternative way of stating this constitutive equation is:
  where
  is the rate-of-strain tensor. So this decomposition can be made explicit as:
  This constitutive equation is also called the Newtonian law of viscosity.
  The total stress tensor  can always be decomposed as the sum of the isotropic stress tensor and the deviatoric stress tensor ():
  In the incompressible case, the isotropic stress is simply proportional to the thermodynamic pressure :
  and the deviatoric stress is coincident with the shear stress tensor :
  The stress constitutive equation then becomes
  or written in more compact tensor notation
  where  is the identity tensor.